Despite all this recent progress, there are still many open questions about the emergence of spacetime near black holes. One such question is to what extent the interior remains smooth for black holes which are sufficiently “typical”. Around ten years ago it was observed in [1]}, [2]}, [3]}, [4]} that there are serious obstacles to realizing a conventional description of the black hole interior in a microscopic theory where the entropy of the black hole is given by (REF ). Some of these obstacles have since been overcome, but the general situation is still unknown and we seem to still be missing some key ingredient. Relatedly we do not yet know how to think about the black hole singularity in a precise way: is there any sharp question we can ask about it, and in particular is there any sense in which sufficiently small objects which fall into it pass through and end up somewhere else? More generally we still have the problem that our best techniques for analyzing black holes in the gravitational variables are still only approximate, so there are boundary observables (such as the black hole S-matrix or the detailed late-time behavior of the spectral form factor) which we are not able to account for using known bulk techniques. One idea is to study such questions using string theory, but string theory remains in most cases only a perturbative framework so doing this would require a deeper formulation of string theory than we currently have.
